1. If the coordinates of a point are (0, -3), it lies on:
Answer:
Explanation:
Any point with x-coordinate as 0 lies on the Y-axis.
2. The coordinates of the origin are:
Answer:
Explanation:
The origin has both x and y coordinates as zero.
3. The distance between the points (3,4) and (3,-4) is:
Answer:
Explanation:
Since the x-coordinates are the same, the distance is the difference of the y-coordinates, which is 8 units.
4. The point equidistant from (2,3), (4,3) and (3,5) is:
Answer:
Explanation:
The point equidistant from three given points will be the circumcenter of the triangle formed by those points.
5. The point (4,-5) lies in:
Answer:
Explanation:
Points with positive x and negative y coordinates lie in the fourth quadrant.
6. If a point P has coordinates (-3,4), then its reflection in the X-axis is:
Answer:
Explanation:
The reflection in the X-axis changes the sign of the y-coordinate while the x-coordinate remains the same.
7. The slope of the line joining the points (2,3) and (4,7) is:
Answer:
Explanation:
Slope = (y2 – y1) / (x2 – x1) = (7 – 3) / (4 – 2) = 2.
8. If the coordinates of the midpoint of the line segment joining the points (x1, y1) and (x2, y2) are (x,y), then x is:
Answer:
Explanation:
The x-coordinate of the midpoint is the average of the x-coordinates of the given points.
9. The y-intercept of the line 3x – 4y = 12 is:
Answer:
Explanation:
The y-intercept is the y-coordinate of the point where the line intersects the Y-axis (x=0). Setting x=0 in the equation gives y = -3.
10. The equation of the X-axis is:
Answer:
Explanation:
The X-axis is a horizontal line, so its equation is y = 0.
11. Which of the following lines is parallel to the X-axis?
Answer:
Explanation:
A line with an equation in the form y = k, where k is a constant, is parallel to the X-axis.
12. The distance between the points (-2,3) and (4,-3) using the distance formula is:
Answer:
Explanation:
Distance = √[(4+2)^2 + (-3-3)^2] = 7√2 units.
13. The coordinates of a point which divides the line segment joining (1,2) and (3,4) internally in the ratio 1:2 are:
Answer:
Explanation:
Using the section formula, the point is [(1*2+3*1)/3, (2*2+4*1)/3] = (5/3,8/3).
14. Which of the following represents a line perpendicular to 3x – 4y = 12?
Answer:
Explanation:
Two lines are perpendicular if the product of their slopes is -1. The slope of 3x – 4y = 12 is 3/4. Hence, a line with slope -4/3 will be perpendicular to it.
15. The area of the triangle with vertices (0,0), (0,4) and (3,0) is:
Answer:
Explanation:
The triangle is right-angled at the origin. Area = 0.5 x base x height = 0.5 x 4 x 3 = 6 square units.
16. The line represented by 2x – y = 0 has a slope of:
Answer:
Explanation:
Rearranging the equation to y = mx + c form, y = 2x. Hence, slope m = 2.
17. If the point (p,q) lies on the line y = 3x, then:
Answer:
Explanation:
For any point on the line y = 3x, the y-coordinate is thrice the x-coordinate.
18. Which of the following is the equation of the Y-axis?
Answer:
Explanation:
The Y-axis is represented by the vertical line where x = 0.
19. The midpoint of the segment joining the points (a,b) and (c,d) is:
Answer:
Explanation:
The coordinates of the midpoint are the averages of the x-coordinates and y-coordinates of the endpoints.
20. The line y = mx + c passes through the origin if:
Answer:
Explanation:
A line passing through the origin will have its y-intercept c = 0.